Generating structure envelopes and using them to facilitate structure determination
A structure envelope (a specific type of periodic nodal surface) can be generated from just a few (typically 1-5) strong, low-index reflections (i.e. precisely those that are least likely to be involved in overlap in a powder diffraction pattern).
An example of such a surface is shown for the zeolite analcime (ANA framework type) here. It was generated using just the 112 reflection (and its symmetry equivalents). Note that all atoms of the framework are located on the blue side of the surface.
More examples of structure envelopes can be viewed by clicking here.
The surface separates the unit cell into regions of high and low electron density, and can be used to facilitate direct space (model-building) structure determination algorithms (e.g. Monte Carlo, Simulated Annealing, Genetic Algorithm, FOCUS). Not only is the volume of the asymmetric unit in which atoms are likely to be located approximately halved, that volume has a shape that severely limits the number of orientations and conformations that a molecule or framework can adopt.
To generate such a surface, the phases of the reflections used must first be determined, and this can be difficult. However, a combination of the Sayre equation, the pseudoatom method and phase permutation has proved to be quite effective.
The option of using a structure envelope to facilitate structure solution has been incorporated into FOCUS (for zeolite structures) and into a Monte Carlo / simulated annealing algorithm (for organic structures). The latter was used to solve the structure of a complex tri-beta-peptide with 17 variable torsion angles from laboratory powder diffraction data.
Supported by the Swiss National Science Foundation.
S. Brenner, L.B. McCusker and Ch. Baerlocher, "Using a structure envelope to facilitate structure solution from powder diffraction data", J. Appl. Cryst. (1997) 30, 1167-1172.
S. Brenner, L.B. McCusker and Ch. Baerlocher, "The application of structure envelopes in structure determination from powder diffraction data:, J. Appl. Cryst. (2002) 35, 243-252.
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